radical
Very extreme or complete change from the usual way.
Radical means going to the root of something or making extreme, fundamental changes. When a scientist proposes a radical new theory, she's suggesting we rethink everything we thought we knew from the ground up. When a city makes radical changes to its traffic system, it's completely redesigning it, not just adding a stop sign here and there.
A radical solution digs down to the root cause of a problem rather than just treating surface symptoms. If your school has a bullying problem, handing out more detentions might help temporarily, but a radical approach would examine why bullying happens and reshape the whole school culture.
In mathematics, a radical is the symbol (√) used to indicate a square root or other root. The radical sign tells you to find what number, multiplied by itself, gives you the number under the symbol.
In politics, someone called a radical wants major, swift changes to how society works, often opposing the way things have traditionally been done. Political radicals throughout history have pushed for everything from democracy to workers' rights to environmental protection, though the label itself doesn't tell you whether their specific ideas are good or bad.
The word can describe ideas, changes, plans, or people. Something radical challenges the status quo and refuses to accept “that's how we've always done it” as a good enough reason to keep doing it that way.